question 11 the crime rate of a certain city is increasing according to the function a = 450e^.04t, where t…

question 11 the crime rate of a certain city is increasing according to the function a = 450e^.04t, where t is the number of years that have passed since the year 2004. round answers to the nearest whole number.... a) determine the approximate number of crimes in the year 2005. b) predict the approximate number of crimes that will occur in the year 2035.

question 11 the crime rate of a certain city is increasing according to the function a = 450e^.04t, where t is the number of years that have passed since the year 2004. round answers to the nearest whole number.... a) determine the approximate number of crimes in the year 2005. b) predict the approximate number of crimes that will occur in the year 2035.

Answer

Explanation:

Step1: Find t for 2005

For the year 2005, $t = 2005 - 2004=1$.

Step2: Calculate number of crimes in 2005

Substitute $t = 1$ into $A = 450e^{0.04t}$, so $A = 450e^{0.04\times1}=450e^{0.04}$. Using a calculator, $e^{0.04}\approx1.04081$, then $A = 450\times1.04081\approx468$.

Step3: Find t for 2035

For the year 2035, $t = 2035 - 2004 = 31$.

Step4: Calculate number of crimes in 2035

Substitute $t = 31$ into $A = 450e^{0.04t}$, so $A = 450e^{0.04\times31}=450e^{1.24}$. Using a calculator, $e^{1.24}\approx3.4514$, then $A = 450\times3.4514\approx1553$.

Answer:

a) 468 b) 1553